Final answer:
A liver cell organelle functioning primarily for the digestion of macromolecules and old organelles would be identified as a lysosome, which contains enzymes to break down and digest these substances.
Step-by-step explanation:
An organelle found in a liver cell would best be identified as a lysosome if its primary function was the digestion of macromolecules and old organelles. Lysosomes are membrane-bound organelles containing hydrolytic enzymes necessary for breaking down various biological polymers such as proteins, polysaccharides, lipids, nucleic acids, and damaged organelles. These organelles play a crucial role in cellular waste disposal, autophagy, and the destruction of pathogens via phagocytosis or endocytosis.